3RD LE - STAT 164

RANDOMIZED EXPERIMENT

a longitudinal study characterized by the presence of experimental units and treatments that are manipulated, randomized or controlled by chance to detect cause-and-effect relationship

RANDOMIZED EXPERIMENT

goal is to see the effect of the treatment or exposure to the response while controlling for other factors

RANDOMIZED EXPERIMENT

In terms of causation, _________________ presents the strongest support to causation.

ADVANTAGES OF EXPERIMENTS

Allow set-up of direct comparison between treatments of interest (_________)

randomization

ADVANTAGES OF EXPERIMENTS

Minimize any bias in the comparison (_____________)

replication

ADVANTAGES OF EXPERIMENTS

Minimize error in the comparison (error control and ____________)

ADVANTAGES OF EXPERIMENTS

____________ are in control of the experiment (experimental vs observational)

 set of experimental procedures or conditions whose effects are to be measured and compared

Treatment Levels

pre-set quantities of a quantitative factor or categories of a qualitative factor

Response Variable

characteristic used to measure the effect of a treatment

Response Variable

the dependent variable or outcome that we observe after applying a treatment to an experimental unit

unit or group of units to which treatment is applied

unit on which the response variable is observed or measured

variation in the observed values of the response variable from experimental units treated alike

variation among sampling units within an experimental unit, and so were also treated alike

Provide the following:

• Treatment/Factor:

• Treatment Levels:

• Response Variable:

• Experimental Unit:

• Sampling Unit:

Provide the following:

• Treatment/Factor:

• Treatment Levels:

• Response Variable:

• Experimental Unit:

• Sampling Unit:

involves the assignment of treatments to the experimental units

practice of deliberately changing or manipulating treatments in a specified manner in order to evaluate the effect of these changes on the response variable

concerned with planning experiments in order to obtain maximum amount of information from the available resources

design structure

Component of the experimental design:

the way we randomly assign our treatment units.

treatment structure

Component of the experimental design:

set of factors or treatment units we want to measure

allows a trmt to be applied and observed more than once and provides an estimate of the experimental error

experimental error

It is the variation among responses of the EU, which cannot be obtained from only one replicate.

ensures trmts will have equal chance of being assigned to an eu that makes the estimate of the experimental error valid

all other means conducted to minimize the experimental error

makes the design efficient and the tests more sensitive and powerful

ANALYSIS OF VARIANCE

a technique that compares the means of a response variable among groups dictated by the treatment levels

ANALYSIS OF VARIANCE

main analytical tool used as a method to compare several means from a randomized experiment

ANALYSIS OF VARIANCE

uses two measures of variances to detect differences among means

Provide the Test of Hypothesis informaiton for ANOVA:

• Ho (in words)

• Ha (in words)

• Test Procedure

• Decision Rule

• And fill in the table:

  

Error

__________ is the difference between the observed response and the model predicted response.

1. quantitative

2. Normality

3. Homoscedasticity

4. Independence

ASSUMPTIONS OF ANOVA

1. Response variable must be ____________

2. __________ of Errors

   • Errors or residuals must be normally distributed with mean equal to zero.

3. ________________of Errors

   • Errors must have constant variance

4. ____________of Errors

   • An error must not depend on another error.

   • Automatically satisfied when randomization is properly performed.

• Normality

  • normally

  • not normally

• Homoscedasticity

  • have constant; homoscedastic

  • do not have constant; heteroscedastic

ASSUMPTIONS OF ANOVA

Test of Hypothesis

• __________ of Errors

  • Ho: The errors are _________ distributed.

  • Ha: The errors are _________ distributed.

• _______________ of Errors

  • Ho: Errors ______________ variance (_______________).

  • Ha: Errors ______________ variance (_______________).

Decision Rule: Reject Ho if p-value ≤ α, oftr Ho.

What is the formula for the computed F-statistic (F_c) in ANOVA?

ANOVA - measures of variances

• __________________: measures variation between treatment levels

• __________________: measures variation between experimental units

COMPLETELY RANDOMIZED DESIGN

most basic experimental design

COMPLETELY RANDOMIZED DESIGN

allocation of treatments is done by randomizing the treatments completely over the entire set of eu’s without any restriction imposed on the units

COMPLETELY RANDOMIZED DESIGN

the only criteria for data classification is the factor/s under test so eu’s must be as homogenous as possible

COMPLETELY RANDOMIZED DESIGN

applicable for both balanced and unbalanced replication

Provide/perform the following:

• Rank the random #s

• Treatment level of each random #

• The final layout

Provide the following:

• Treatment/Factor:

• Treatment Levels:

• Response Variable:

• Experimental Unit:

• Sampling Unit:

What is the formula for a Linear Model for a single factor CRD?

Also Provide the following:

• Decision:

• Conclusion:

PAIRWISE MEAN COMPARISON

_______________ - compares ALL possible pairs of treatment means and tests if they are significantly different.

• For example, in the aquaculture example you would have: AvsB, BvsC, CvsD, AvsC, AvsD, BvsD
  

Provide also the Ho and Ha of this in words.

RANDOMIZED COMPLETE BLOCK DESIGN

Blocks

____________________________

• assumes that another single factor aside from the treatment is classifying the experimental units

  • eu’s are grouped into r blocks

  • The variability among the blocks is taken out of the experimental error thereby improving the precision of the experiment.

__________

• groups of eu’s that are more or less homogeneous

Provide the following:

• Treatment/Factor:

• Treatment Levels:

• Blocking Factor:

• Experimental Unit:

• Sampling Unit:

• Response Variable:

Provide Ho and Ha in words for the TEST ON VARIETY EFFECT and fill in the blanks:

Then provide the decision and conclusion.

Provide Ho and Ha in words for the TEST ON BLOCK EFFECT and fill in the blanks:

Then provide the decision and conclusion.

FACTORIAL DESIGN

Most efficient for experiments involving two or more factors whose levels are often said to be crossed to allow interaction

FACTORIAL DESIGN

In each complete trial of the experiment, all possible combinations of the levels of the factors are investigated.

FACTORIAL DESIGN

Ex. If there are 3 levels for Factor A, 4 levels for Factor B, and 2 levels for Factor C, then each experiment contains all 3 x 4 x 2 = 24 trmt combinations.

Provide the following:

• Experimental Design

• Treatment/Factor:

• Treatment Combination:

• Experimental Unit:

• Response Variable:

Provide Ho and Ha in words for the Test on two-way interaction effect and fill in the blanks:

Then provide the decision and conclusion.

Provide Ho and Ha in words for the Test on main effect of Soil Type.

Then provide the decision and conclusion.

Provide Ho and Ha in words for the Test on main effect of Period.

Then provide the decision and conclusion.

CHI-SQUARE TEST

considered as the most commonly used member of the non-parametric family of tests that deals with counts or frequencies

CHI-SQUARE TEST

does not require assumptions about parameters (mean or variance) nor test hypotheses about population parameters

CHI-SQUARE GOODNESS-OF-FIT TEST

Which Analysis of Count Data?

An agriculturist wants to determine if the reported proportions of adults who said that genetically modified food was safe (35%), not safe (52%) or no opinion at all (13%) are true in their locality

CHI-SQUARE GOODNESS-OF-FIT TEST

Which Analysis of Count Data?

The percentage of Americans with each blood type are as follows: 0 (43%), A (40%), B (12%), and AB (5%). Red Cross Organization wants to check if the Filipino population follows the same divisions.

CHI-SQUARE GOODNESS-OF-FIT TEST

Which Analysis of Count Data?

Investigating if the observed phenotypic ratios in a dihybrid cross of heterozygous individuals follow the expected 9:3:3:1 ratio.

CHI-SQUARE GOODNESS-OF-FIT TEST

Which Analysis of Count Data?

Determining whether cats equally prefer different brands of cat food. Will the preference for each of the 5 brands of cat food be equal, with 20 cats preferring each brand, among a group of 100 cats?

CHI-SQUARE GOODNESS-OF-FIT TEST

used to test whether a frequency distribution fits a specific pattern

Assumption

• The expected frequency for each category must be at least 5.

CHI-SQUARE GOODNESS-OF-FIT TEST

determines whether observed frequencies of a categorical data collected from a single sample matches the expected distribution.

• Tests only a single sample/set of samples

CHI-SQUARE GOF TEST, Test of Hypothesis

provide the following:

• Ho (in words):

• Ha (in words):

• Test Procedure:

• Test Statistic:

• Decision Rule:

CHI-SQUARE GOF TEST, provide the following:

• Ho (in words):

• Ha (in words):

• Decision Rule:

• Test Statistic:

Then provide the following:

• Decision:

• Conclusion:

CHI-SQUARE GOF TEST, provide the following:

• Ho (in words):

• Ha (in words):

• Decision Rule:

• Test Statistic:

Then provide the following:

• Decision:

• Conclusion:

CHI-SQUARE TEST OF HOMOGENEITY

Which Analysis of Count Data?

A geneticist wanted to determine if the distribution of phenotypic traits is consistent or different between two groups of individuals, each group having a unique genotype.

CHI-SQUARE TEST OF HOMOGENEITY

Which Analysis of Count Data?

There are three possible behaviors that may occur when dogs are subjected to a certain stimulus. An animal behavior researcher wanted to know if the proportions of these three behaviors are equal between domesticated dogs and wild dogs.

CHI-SQUARE TEST OF HOMOGENEITY

Which Analysis of Count Data?

To understand patterns of biodiversity, a study investigated whether the number of species is consistent among different types of habitat

CHI-SQUARE TEST OF HOMOGENEITY

Which Analysis of Count Data?

In a clinical trial, the response to a new drug was tested between blood cancer patients and skin cancer patients. They observed if the drug will be effective with adverse effects, effective without adverse effects, ineffective with adverse effects, or ineffective without adverse effects.

CHI-SQUARE TEST OF HOMOGENEITY

used to test whether the proportions for a variable are equal when several samples are selected from different and independent populations

• CHI-SQUARE TEST OF HOMOGENEITY

• CHI-SQUARE TEST OF INDEPENDENCE

CHI-SQUARE TEST OF HOMOGENEITY, Test of Hypothesis

provide the following:

• Ho (in words):

• Ha (in words):

• Test Procedure:

• Test Statistic:

• Decision Rule:

CHI-SQUARE TEST OF HOMOGENEITY, provide the following:

• Ho (in words):

• Ha (in words):

• Decision Rule:

• Test Statistic:

Then provide the following:

• Decision:

• Conclusion:

CHI-SQUARE TEST OF HOMOGENEITY, provide the following:

• Ho (in words):

• Ha (in words):

• Decision Rule:

• Test Statistic:

Then provide the following:

• Decision:

• Conclusion:

CHI-SQUARE TEST OF INDEPENDENCE

Which Analysis of Count Data?

A researcher wishes to determine whether there is a relationship between the gender of an individual and the amount of alcohol consumption (low, moderate, high).

CHI-SQUARE TEST OF INDEPENDENCE

Which Analysis of Count Data?

A wildlife conservationist wanted to assess whether the class of vertebrate is associated with whether it is endangered or threatened

CHI-SQUARE TEST OF INDEPENDENCE

Which Analysis of Count Data?

An inheritance study wanted to determine whether presence of genetic markers is associated with the stages of a specific disease.

CHI-SQUARE TEST OF INDEPENDENCE

Which Analysis of Count Data?

A clinical trial assessed whether there is significant association between the dose of a drug and the occurrence of adverse side effects.

CHI-SQUARE TEST OF INDEPENDENCE

• also called Chi-square Test of Associatio

• hypothesizes about the presence of a relationship or association between two qualitative variables observed from a single sample.

independent groups; related variables

If Chi-square test of homogeneity uses _____________, Chi-square test of independence uses _____________ since both were observed from a single set of units.

CHI-SQUARE TEST OF INDEPENDENCE, Test of Hypothesis

provide the following:

• Ho (in words):

• Ha (in words):

• Test Procedure:

• Test Statistic:

• Decision Rule:

CHI-SQUARE TEST OF HOMOGENEITY, provide the following:

• Ho (in words):

• Ha (in words):

• Decision Rule:

• Test Statistic:

Then provide the following:

• Decision:

• Conclusion:

CHI-SQUARE TEST OF HOMOGENEITY, provide the following:

• Ho (in words):

• Ha (in words):

• Decision Rule:

• Test Statistic:

Then provide the following:

• Decision:

• Conclusion:

What is the condition needed for each of the following measures of association and their corresponding formula?

• Phi coefficient

• Contingency coefficient

• Cramer’s V

Solve and interpret for the appropriate measures of association.

CORRELATION ANALYSIS

It is a statistical technique used to determine the strength of the relationship between two variables, X and Y.

CORRELATION ANALYSIS

it provides a measure of strength of the linear relationship between two variables measured in at least interval scale.

SCATTER PLOT

• a graph of the ordered pairs of numbers consisting of variables X and Y

• a visual way to describe the nature of the relationship between two quantitative variables

Correlation Coefficient

• It is a quantitative measure of the closeness or degree of relationship between two variables

• It can be computed using a particular formula depending on the characteristic of the variable of interest

What do the following ρ ranges mean?

• ρ > 0

• ρ < 0

• ρ = 0

How about the Strength of Linear Relationship?

• Provide range and then interpretation for each.

If its ordinal we automatically cant use Pearson’s

What are the assumptions for PEARSON’S CORRELATION ANALYSIS?

1. Both variables must follow the _______________.

   • What test?

     • Ho (in words):

     • Ha (in words):

2. The variables must be measured at least in the ______________ or must be ______________.